Operator Product Expansions and Consistency Relations in a O(N) Invariant Fermionic CFT for 2<d<4

TL;DR

This paper investigates an O(N) symmetric Majorana fermion conformal field theory in dimensions between 2 and 4, using operator product expansions and consistency relations to compute critical couplings and anomalous dimensions.

Contribution

It introduces a novel approach employing OPEs and shadow singularity cancellations to analyze fermionic CFTs in non-integer dimensions, providing new calculations of critical couplings and anomalous dimensions.

Findings

Calculated the critical coupling G_{*} to leading order in 1/N.

Reproduced the O(1/N) correction for the fermion anomalous dimension.

Validated the approach for conformal field theories in d>2.

Abstract

A conformally invariant theory of Majorana fermions in 2<d<4 with O(N) symmetry is studied using Operator Product Expansions and consistency relations based on the cancellation of shadow singularities. The critical coupling G_{*} of the theory is calculated to leading order in 1/N. This value is then used to reproduce the O(1/N) correction for the anomalous dimension of the fermion field as evidence for the validity of our approach to conformal field theory in d>2.